Home
Class 12
MATHS
Show that y=a*e^(2x)+b*e^(-x) is a solut...

Show that `y=a*e^(2x)+b*e^(-x)` is a solution of the differential equation `(d^(2)y)/(dx^(2))-(dy)/(dx)-2y=0`.

Text Solution

Verified by Experts

`y=ae^(2x) +be ^(-x).............(1)`
`(dy)/(dx)=2ae^(2x)-be^(-x).............(2)`
`(d^2y)/(dx^2)=4ae^(2x)+be^(-x).............(3)`
putting values on LHS
`=(d^2y)/(dx^2)-(dy)/(dx)-2y`
`=(4ae^(2x)+be^(-x))-(2ae^(2x)-be^(-x))-2(ae^(2x)+be^(-x))`
`=4ae^(2x) +be^(-x)-2ae^(2x)+be^(-x)-2ae^(2x)-2be^(-x)`
`=0`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • SAMPLE PAPER 2019

    XII BOARD PREVIOUS YEAR PAPER ENGLISH|Exercise Section B 24A|1 Videos

  • SAMPLE PAPER 2019

    XII BOARD PREVIOUS YEAR PAPER ENGLISH|Exercise Section B 24B|1 Videos

  • SAMPLE PAPER 2019

    XII BOARD PREVIOUS YEAR PAPER ENGLISH|Exercise Section B 21 B|1 Videos

  • EXAM REVISION SERIES

    XII BOARD PREVIOUS YEAR PAPER ENGLISH|Exercise All Questions|19 Videos

  • XII Boards

    XII BOARD PREVIOUS YEAR PAPER ENGLISH|Exercise All Questions|255 Videos

Similar Questions

Explore conceptually related problems

Show that y=a e^(2x)+b e^(-x) is a solution of the differential equation (d^2y)/(dx^2)-((dy)/(dx))-2y=0.

Show that y=b e^x+c e^(2x)\ is a solution of the differential equation (d^2y)/(dx^2)-3(dy)/(dx)+2y=0.

Verify that y=ae^(3x)+be^(-x) is a solution of differential equation (d^2y)/(dx^2)-2(dy)/(dx)-3y=0

Show that y=e^(2x) is a solution of differential equation (d^(2)y)/(dx^(2))+(dy)/(dx)-6y=0

Show that x y=a e^x+b e^(-x)+x^2 is a solution of the differential equation x(d^2y)/(dx^2)+2dy/dx-x y+x^2-2=0.

Show that y=acos(logx)+bsin(logx) is a solution of the differential equation x^2(d^2y)/(dx^2)+(dy)/(dx)+y=0.

Show that \ y=A e^(B x) is as solution of the differential equation (d^2y)/(dx^2)=1/y((dy)/(dx))^2dot

Show that y=e^x(A\ cos x+Bsinx) is the solution of the differential equation (d^2y)/(dx^2)-2(dy)/(dx)+2y=0.

Show that y=e^x(A\ cos x+Bsinx) is the solution of the differential equation (d^2y)/(dx^2)-2(dy)/(dx)+2y=0.

The solution of the differential equation ((x+2y^3)dy)/(dx)=y is

Home
Profile